Course Name Code Semester T+U Hours Credit ECTS
Divergence Series MAT 506 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. METİN BAŞARIR Course Lecturers Course Assistants Course Category Course Objective To apprehend the properties of infinite series and infinite products,series with random terms,absolute and conditional convergent series,Riemann Theorem,to understand the numerical calculation of series,product of infinite series,to learn the power series,complex sequences and series,Abel and Drichlet criteria,sequence of variable elements, discrete and uniform convergence. Course Content Infinite series and infinite products(infinite series and convergence,series with positive elements,convergence criterias),The series with random elements(Leibnitz criteria),absolute and conditional convergent series,Riemann Theorem,the numerical calculation of series,product of infinite series,the power series(convergence domain and radius),complex sequences and series,Abel and Drichlet criteria,sequence of variable elements, discrete and uniform convergence,infinite products,Cauchy condition and absolute convergence,some attentions on divergence series,operations of limiting,operations C-,H-;operation of A-,operation of E-;
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she recognizes the properties of infinite series and infinite products. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
2 He/she distinguishes the series with random terms,absolute and conditional convergent series. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
3 He/she expresses the discrete and uniform convergence. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
4 He/she recognizes complex sequences and series . Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
5 He/she expresses Abel and Drichlet criteria. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
6 He/she recognizes and interprets the sequence of variable elements. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
7 He)she calculates the series numerically. Lecture, Question-Answer, Discussion, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Infinite series and infinite products
2 Infinite series and convergence,series with positive elements,convergence criterias
3 The series with random elements
4 Leibnitz criteria,absolute and conditional convergent series
5 Riemann Theorem, the numerical calculation of series,
6 Product of infinite series
7 The power series,convergence domain and radius
8 Complex sequences and series, Abel and Drichlet criterias
9 intermediate examination
10 Sequence of variable elements, discrete and uniform convergence,
11 Infinite products,Cauchy condition and absolute convergence,
12 Some attentions on divergence series,operations of limitİNG
13 operations C-,H-;operation of A-,operation of E-;
14 operation of A-,operation of E-;
Resources
Course Notes [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul
Course Resources [2] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London.
[3] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul
[4] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.
Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Ödev 20
1. Kısa Sınav 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100